dolfin team mailing list archive

[Martin Sandve Alnæs <martinal@xxxxxxxxx>]

Not a linear form, but a functional. That's what norm does anyway.

u = Function(element)
x, y, z = tetrahedron.x
L2 = (sin(2*pi*x) - u)**2*dx

You still have to make sure you compile
with sufficient quadrature order though.

Martin



On Wed, Jun 10, 2009 at 6:33 PM, Shawn Walker<walker@xxxxxxxxxxxxxxx> wrote:
> Actually, I have a question about this.  I may have asked this before, so
> forgive me if I repeat.
>
> Suppose my exact solution is sin(2*pi*x).  I would like to compute the exact
> error against this function.  Is this doable?  I know you can resample it
> with a higher order function, but that is lame!  Can't FFC treat it like a
> linear form and use quadrature to evaluate it?  I know it isn't really a
> linear form, but FFC wouldn't know the difference!  :) Maybe I am missing
> something...
>
> - Shawn
>
> On Wed, 10 Jun 2009, Martin Sandve Alnæs wrote:
>
>> The norm definitions should use "inner" instead of "dot" to handle
>> tensor fields as well.
>>
>> Martin
>>
>>
>>
>> On Wed, Jun 10, 2009 at 6:14 PM, Anders Logg<logg@xxxxxxxxx> wrote:
>>>
>>> On Wed, Jun 10, 2009 at 09:58:20AM -0500, Jehanzeb Hameed wrote:
>>>>
>>>> Thanks. So I guess that means no such facility is available in C/C++ ?
>>>
>>> No, since the computation depends on the space the functions are in
>>> and so the code needs to be generated. In C++, you need to define a
>>> form file for the norm. Look at
>>>
>>>  site-packages/dolfin/norm.py
>>>
>>> for how to define the norms.
>>>
>>> --
>>> Anders
>>>
>>>
>>>> On Wed, Jun 10, 2009 at 2:03 AM, Anders Logg<logg@xxxxxxxxx> wrote:
>>>>>
>>>>> On Tue, Jun 09, 2009 at 05:11:48PM -0500, Jehanzeb Hameed wrote:
>>>>>>
>>>>>> Hello,
>>>>>>
>>>>>> Is there a builtin function in dolfin to compute L^2 or H_1 norms? If
>>>>>> so, can you please point it out. If not, are there support functions
>>>>>> (e.g. a Gauss Quadrature table, computation of Jacobians, etc) which
>>>>>> can help in this?
>>>>>
>>>>> Yes, this is available in the DOLFIN Python interface:
>>>>>
>>>>>  norm(v)
>>>>>
>>>>> The default computes the L^2 norm. Several options are available:
>>>>>
>>>>>  L^2:     norm(v, 'L2')
>>>>>  H^1:     norm(v, 'H1')      includes L^2 term
>>>>>  H^1_0:   norm(v, 'H10')     does not include L^2 term
>>>>>  H(div):  norm(v, 'Hdiv')    includes L^2 term
>>>>>  H(div):  norm(v, 'Hdiv0')   does not include L^2 term
>>>>>  H(curl): norm(v, 'Hcurl')   includes L^2 term
>>>>>  H(curl): norm(v, 'Hcurl0')  does not include L^2 term
>>>>>
>>>>>
>>>>> -----BEGIN PGP SIGNATURE-----
>>>>> Version: GnuPG v1.4.9 (GNU/Linux)
>>>>>
>>>>> iEYEARECAAYFAkovWqUACgkQTuwUCDsYZdGb3gCfa2gWnzealWzkjPoRj8hf3cr/
>>>>> 0EUAoJh4mpaIzRU9eCnnC+XWlupu6SV0
>>>>> =so4c
>>>>> -----END PGP SIGNATURE-----
>>>>>
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>>> -----BEGIN PGP SIGNATURE-----
>>> Version: GnuPG v1.4.9 (GNU/Linux)
>>>
>>> iEYEARECAAYFAkov28sACgkQTuwUCDsYZdE8KQCdEI7wS27QaNw9knI2U9L+RVST
>>> xeUAnRdLrrhAVzsBn6nO1b6CLEpF64ey
>>> =a7iu
>>> -----END PGP SIGNATURE-----
>>>
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